Equalizer and detector arrangement employing joint entropy-based calibration

ABSTRACT

An equalizer configured to receive a data signal from a channel. The detector is coupled to the equalizer, and a calibration unit is coupled with the equalizer and the detector. The calibration unit is configured to jointly calibrate the equalizer and the detector using a metric subject to an entropy-preserving equalizer constraint.

SUMMARY

Embodiments of the disclosure are directed to an apparatus whichincludes an equalizer configured to receive a data signal from achannel. A detector is coupled to the equalizer, and a calibration unitis coupled with the equalizer and the detector. The calibration unit isconfigured to jointly calibrate the equalizer and the detector using ametric subject to an entropy-preserving equalizer constraint.

Various method embodiments involve receiving a data signal from achannel, equalizing the data signal using an equalizer, and detecting auser information component of the data signal. Method embodiments alsoinvolve calibrating the equalizer and the detector jointly using ametric subject to an entropy-preserving equalizer constraint.

These and other features and aspects which characterize variousembodiments can be understood in view of the following detaileddiscussion and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates various processes for jointly calibrating anequalizer and a detector coupled to a channel in accordance with variousembodiments;

FIG. 2 shows various processes for jointly calibrating an equalizer anda detector coupled to a channel in accordance with other embodiments;

FIG. 3 shows an apparatus for performing joint calibration using anentropy-based metric in accordance with various embodiments;

FIG. 4 shows an apparatus for performing joint calibration using anentropy-based metric in accordance with other embodiments;

FIG. 5 shows an embodiment of an apparatus for performing jointcalibration using an entropy-based metric in accordance with variousembodiments; and

FIG. 6 shows an embodiment of an apparatus for performing jointcalibration using an entropy-based metric in accordance with otherembodiments.

DETAILED DESCRIPTION

Embodiments of the disclosure are directed to equalizer and detectorarrangements for processing data signals transmitted through a channel.Embodiments of the disclosure are directed to jointly calibrate anequalizer and a detector using a metric subject to an entropy-preservingequalizer constraint. Jointly calibrating the equalizer and the detectorpreferably involves producing a decomposition that satisfies theentropy-preserving equalizer constraint, such as by producing thedecomposition using a causal factor, an anticausal factor, and a delayfactor.

The metric is preferably an entropy-based metric. For example, themetric can be representative of a statistical distance measure (e.g., aKullback-Leibler (KL) distance or relative entropy) between a modeledprobability distribution functions (PDF) and an actual channel PDF,which is unknown. Jointly calibrating the equalizer and detectorinvolves determining a PDF from a class of modeled PDFs using thestatistical distance measure (e.g., minimum relative entropy (MRE)).

Particular embodiments are directed to using an MRE metric to jointlyimplement a finite impulse response (FIR) equalizer and a soft outputViterbi algorithm (SOVA) detector coupled to a channel. While manyembodiments described herein use an MRE metric, other embodiments canuse any entropy-based metric that represents a statistical distancebetween a modeled PDF and the actual channel PDF. The channel can be anykind of channel, such as a communication channel or a read channel of adata storage device (e.g., a magnetic recording device).

Embodiments of the disclosure eliminate the need for a partial responsetarget and target optimization. Various embodiments are directed to anapparatus comprising an equalizer configured to receive a data signalhaving inter-symbol interference from a channel and a detector coupledto the equalizer, wherein the detector and equalizer are configured tooperate cooperatively to decode a user information component from thedata signal without using a partial response target. Some embodiments ofthe disclosure provide for enhanced equalization signal-to-noise ratio(SNR) performance for a fixed complexity SOVA detector. Implementing aFIR equalizer and SOVA detector arrangement according to variousembodiments involves use of training data at operating noise.

According to various embodiments of the disclosure, a data signalcomprising a user information component is transmitted through a channeland received at a receive location. An equalizer, a detector, and acalibration unit are provided at the receive location and operatecooperatively to detect the user information component that can bedistorted by the channel. The equalizer is configured to performequalization to remove the effect of the channel from the receivedsignal, in particular inter-symbol interference (ISI) and data-dependentnoise. The detector is configured to detect the user informationcomponent from the equalized signal. In various embodiments, theequalizer is implemented using a linear FIR filter calibrated tominimize the variance of the error signal, and the detector comprises aSOVA module. The calibration unit is configured to calibrate theequalizer and the detector jointly using the entropy-based metric forenhancing detection accuracy.

A typical conventional approach to designing a FIR equalizer and SOVAdetector involves a two-step training process. First, the equalizerfilter is trained or calibrated to minimize the mean square error (MSE)of the equalization error with respect to a fixed partial response (PR)target filter. The PR target is chosen by trial and error. Then, theSOVA detector uses a data-dependent noise prediction (DDNP) model thatis calibrated to minimize the individual noise variances. The DDNP modelcomprises a whitening filter and a mean shift for each transition in atrellis construct for the SOVA detector. Using this two-step calibrationapproach, the FIR equalizer is chosen by an exhaustive search overinteger targets followed by simulation.

Embodiments of present disclosure are directed to finding the best FIRequalizer and DDNP model jointly without binding the model to a PRtarget. An entropy-based metric, such as minimum relative entropy, isused to jointly design the equalizer and the DDNP model parameters in acomputationally efficient way. The joint calibration scheme enhances(e.g., optimizes) performance of the equalizer and the detector,preferably with a one-step calibration and without using a PR target.According to various embodiments, a useful design metric is one thatprovides for a minimum relative entropy or a minimum Kullback-Leibler(KL) distance between a determined PDF of a modeled channel and a PDF ofthe actual channel.

According to various embodiments, methods for jointly calibrating anequalizer and a detector based on the entropy-based metric involvereceiving a data signal from a channel by an equalizer, equalizing thedata signal using the equalizer, and detecting a user informationcomponent of the data signal. According to some embodiments, methods forjointly calibrating an equalizer and a detector involve receiving anequalized signal from the equalizer, implementing a Viterbi algorithmand a trellis construct comprising states and transitions among thestates, implementing a data-dependent noise predictive (DDNP) model,whitening a signal and storing mean shifts for each transition in thetrellis construct, performing an estimation of the user informationcomponent, determining a modeled PDF from a class of modeled PDFs, andproviding updates to the equalizer and the detector adaptively andsubstantially in real-time.

In accordance with other embodiments, apparatuses for performing jointcalibration using an entropy-based metric, such as an MRE metric,include an equalizer configured to receive a data signal from a channel,a detector coupled to the equalizer, and a calibration unit coupled withthe equalizer and the detector, the calibration unit configured tojointly calibrate the equalizer and the detector using the MRE metric.According to some embodiments, apparatuses for performing jointcalibration using minimum relative entropy include a detector comprisinga soft output Viterbi algorithm (SOVA) module and a data-dependent noisepredictive (DDNP) module coupled with the SOVA module. The SOVA moduleis configured to implement a Viterbi algorithm and a trellis constructcomprising states and transitions among the states. The DDNP modulecomprises a whitening filter and a storage device configured to storemean shifts for each transition in the trellis construct. According tosome embodiments, apparatuses for performing joint calibration using MREinclude an equalizer comprising a causal equalizer and an anti-causalequalizer, and a calibration unit comprising an adaptive algorithmmodule configured to provide updates to the equalizer and the detectorwith an adaptive MRE architecture.

Referring now to FIG. 1, there is illustrated various processes forjointly calibrating an equalizer and a detector coupled to a channel inaccordance with various embodiments. The method illustrated in FIG. 1involves receiving 110 a data signal from a channel by an equalizer. Thedata signal comprises a user information component to be detected. Themethod further includes equalizing 120 the data signal using theequalizer, and detecting 130 the user information component of the datasignal by a detector. The equalizer and detector are calibrated jointly140 using a metric subject to an entropy-preserving equalizerconstraint. The joint calibration methodology according to variousembodiments obviates the need to use a partial response target.

FIG. 2 shows various processes for jointly calibrating an equalizer anda detector in accordance with embodiments of the disclosure. The methodshown in FIG. 2 involves receiving 110 a data signal from a channel byan equalizer. The data signal comprises inter-symbol interference (ISI)and a data-dependent noise component. After equalizing 120 the datasignal using the equalizer, the effect of the ISI is removed. To detecta user information component of the data signal, the method of FIG. 2further involves receiving 230 an equalized signal from the equalizerand performing 238 an estimation of the user information component.

According to various embodiments, estimating 238 the user informationcomponent with enhanced accuracy involves implementing 232 a Viterbialgorithm, a trellis construct comprising states and transitions amongthe states, and a data-dependent noise predictive (DDNP) model 234. TheViterbi algorithm is used to determine the most likely Viterbi path bycalculating the probability of a sequence of transitions among states.The DDNP model makes use of the data-dependent noise component of thesignal to support Viterbi path metric calculations. Before performing238 the estimation, a signal is whitened 236 to reduce auto-correlation,and mean shifts for each transition in the trellis construct are stored237 for the calibration (next round update). After the user informationcomponent is detected 238, the equalizer and the detector are calibratedto enhance the accuracy of a subsequent detection operation (next rounddetection).

According to various embodiments, the method illustrated in FIG. 2involves determining 240 a modeled PDF from a class of modeled PDFsusing a statistical distance measure between the modeled PDF and theactual channel PDF. The determined PDF preferably has the minimumKullback-Leibler (KL) distance to the actual channel PDF. The metricused to determine this PDF is called minimum relative entropy. The MREmetric is used to find a PDF matching the channel PDF as close aspossible, to jointly design the equalizer and the detector. Finally,updates are preferably provided 242 to the equalizer and the detectoradaptively and substantially in real-time.

In accordance to various embodiments, the equalizer is configured toperform equalization without using a partial response target. A jointcalibration approach consistent with embodiments of the disclosureoptimizes the equalizer and the detector with no need for a conventionaltwo-step calibration. The method according to FIG. 2 can be applied toany channel, and thus can be viewed as a universal approach. The datasignal can be acquired from a communication channel, for example, orcomprise a read-back signal acquired from a magnetic recording medium.

Various entropy-based design methodologies are contemplated, includingthose that use a numerical MRE design algorithm and those that use anadaptive MRE design algorithm. In general terms, a numericalentropy-based design algorithm is a computationally efficientsemi-analytical solution, where each step of the iteration has ananalytical solution. A numerical MRE design algorithm, for example,works iteratively by repeating the following processes until convergenceoccurs: (a) pivot the equalizer to optimize the DDNP model, then pivotthe DDNP model to re-optimize the equalizer. A numerical MRE designapproach is suitable for off-line calibration since it requires all thetraining data to be available and is computationally demanding. Anumerical MRE design algorithm is typically not suitable for real-timeimplementation, such as in a magnetic recording device incorporated in acomputer system or an active communication channel.

An adaptive MRE design algorithm is suitable for real-time applications.For implementations that employ an adaptive MRE design algorithm, a“suboptimal” MRE metric is used. Although producing a so-called“suboptimal” MRE metric, an adaptive MRE design algorithm has lowerimplementation complexity and virtually the same detection performanceas a numerical MRE design algorithm that produces an “optimal” MREmetric. A representative “suboptimal” MRE metric is described belowunder the heading Minimum Relative Entropy Design.

Representative Joint Calibration Approach:

FIG. 3 shows an apparatus 300 for performing joint calibration usingminimum relative entropy in accordance with various embodiments. Theapparatus 300 shown in FIG. 3 includes an equalizer 320 and a detector330 coupled to the equalizer 320. The equalizer 320 receives a datasignal from a channel 310. The apparatus 300 further includes acalibration unit 340 coupled with the equalizer 320 and the detector330. The calibration unit 340 is configured to jointly calibrate theequalizer 320 and the detector 330 using the MRE metric. A more detaileddescription of the MRE design according to various embodiments isprovided below.

Relative Entropy:

With continued reference to FIG. 3, let the actual (uncharacterized)channel 310 and its modeled PDFs be denoted by:

P(x ₁ ^(N) , y ₁ ^(N))=P(x ₁ ^(N))P(y ₁ ^(N) |x ₁ ^(N)) (actual channel)

{tilde over (P)}(x ₁ ^(N) , y ₁ ^(N))=P(x ₁ ^(N)){tilde over (P)}(y ₁^(N) |x ₁ ^(N)) (modeled channel)

According to embodiments where the channel is a read channel, forexample, x (305) represents channel bits, y (315) represents a read-backsignal, z (325) represents an equalized signal, and {circumflex over(x)} (335) represents detected bits.

The best PDF, {tilde over (P)}∈

, in a given class of PDFs,

, is the one that minimizes the relative entropy (or KL distance), asgiven by:

${\arg \; {\min\limits_{\overset{\sim}{P} \in }{- {\sum\limits_{x_{1}^{N}}{\int_{y_{1}^{N}}{{P\left( {x_{1}^{N},y_{1}^{N}} \right)}{\log \left\lbrack \frac{\overset{\sim}{P}\left( y_{1}^{N} \middle| x_{1}^{N} \right)}{P\left( y_{1}^{N} \middle| x_{1}^{N} \right)} \right\rbrack}{y_{1}^{N}}}}}}}} = {{\arg \; {\max\limits_{\hat{P} \in }{E\; {\log \left\lbrack \frac{\overset{\sim}{P}\left( y_{1}^{N} \middle| x_{1}^{N} \right)}{P\left( y_{1}^{N} \middle| x_{1}^{N} \right)} \right\rbrack}}}} = {\arg \; {\max\limits_{\hat{P} \in }{E\; \log \; {\overset{\sim}{P}\left( y_{1}^{N} \middle| x_{1}^{N} \right)}}}}}$

Problem Formulation:

The equalized signal z=f★y (where ★ denotes convolution or filtering) ismodeled as a signal-dependent Gaussian autoregressive (SDAR) process,given by:

$\mspace{20mu} {{\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)} = {\prod\limits_{n}{\overset{\sim}{P}\left( {\left. z_{n} \middle| z_{n - L}^{n - 1} \right.,x_{n - M}^{n}} \right)}}}$${\overset{\sim}{P}\left( {\left. z_{n} \middle| z_{n - L}^{n - 1} \right.,T_{n}} \right)} = {\frac{1}{\sqrt{2\pi \; {\sigma^{2}\left( T_{n} \right)}}}{\exp\left( {{- \frac{1}{2{\sigma^{2}\left( T_{n} \right)}}}{{{\sum\limits_{l = 0}^{L}{{w_{l}\left( T_{n} \right)}z_{n - l}}} - {\mu \left( T_{n} \right)}}}^{2}} \right)}}$

where the transition pattern is given by: T_(n)=x_(n) ^(n)−M, thevariance is given by α²(T_(n)), whitening filter taps are given byw₁(T_(n)), and means shift is given by μ(T_(n)). We seek the parameters(FIR equalizer and DDNP model) that minimize the relative entropymetric.

Technical Result:

Lemma: Let z=f★y for a stable filter f. Then:

${\frac{1}{N}\log \; {\overset{\sim}{P}\left( z_{1}^{N} \right)}} = {{\frac{1}{N}\log \; {\overset{\sim}{P}\left( y_{1}^{N} \right)}} - {\log \; f_{o}}}$${\log \; f_{o}} = {\frac{1}{2\pi}{\int_{- \pi}^{\pi}{\log {{F(\omega)}}{\omega}}}}$

where f_(o)=f_(mp[)0] is the leading tap of the minimum phase spectralfactor of |F_(mp)(ω)|²=|F(ω)|².

The same result also holds for conditional PDFs:

${\frac{1}{N}\log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}} = {{{\frac{1}{N}\log \; {\overset{\sim}{P}\left( y_{1}^{N} \middle| x_{1}^{N} \right)}} - {\log \; {f_{o}\frac{1}{N}}\underset{\underset{{To}\mspace{14mu} {be}\mspace{14mu} {maximized}}{}}{E\; \log \; {\overset{\sim}{P}\left( y_{1}^{N} \middle| x_{1}^{N} \right)}}}} = {{\frac{1}{N}E\; \log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}} + {\log \; f_{o}}}}$

Minimum Relative Entropy Design:

The problem can be re-casted as a joint maximization:

$\arg \; {\max\limits_{f,{\overset{\sim}{P} \in P}}\left\lbrack {{\frac{1}{N}E\; \log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}} + {\log \; f_{\circ}}} \right\rbrack}$

Given a sufficiently long training sequence, we can drop the expectation(Shannon-McMillan-Breiman Theorem) above:

$\arg \; {\max\limits_{f,{\overset{\sim}{P} \in P}}\left\lbrack {{\frac{1}{N}\; \log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}} + {\log \; f_{\circ}}} \right\rbrack}$

The term log f_(o) ensures that we don't obtain the trivial solutionf=0. In fact, the above problem is equivalent to:

${\arg \; {\max\limits_{f,{\overset{\sim}{P} \in P}}{\log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}\mspace{14mu} {subject}\mspace{14mu} {to}\mspace{14mu} f_{\circ}}}} = 1$

The problem can be written as a nested maximization:

${\max\limits_{f}{\max\limits_{\overset{\sim}{P} \in P}{\log \; {\overset{\sim}{P}\left( z_{1}^{N} \middle| x_{1}^{N} \right)}\mspace{14mu} {subject}\mspace{14mu} {to}\mspace{14mu} f_{\circ}}}} = 1$

For a given f, the standard DDNP training already solves the innerminimization. It can be shown that the outer problem reduces to:

$f_{MRE} = {{\arg \; {\min\limits_{f}{\frac{1}{N_{T}}{\sum\limits_{T}{\frac{1}{2}\log \; {\sigma^{2}(T)}\mspace{14mu} {subject}\mspace{14mu} {to}\mspace{14mu} f_{\circ}}}}}} = 1}$

For a suboptimal metric suitable for use in a real-time adaptiveimplementation (e.g., a communication channel or a read channel of amagnetic recording system), the logarithm can be dropped to minimize theaverage DDNP variance instead:

$f_{MRE} = {{\arg \; {\min\limits_{f}{\frac{1}{N_{T}}{\sum\limits_{T}{\frac{1}{2}\; {\sigma^{2}(T)}\mspace{14mu} {subject}\mspace{14mu} {to}\mspace{14mu} f_{\circ}}}}}} = 1}$

Equalizer Decomposition:

Various embodiments of the disclosure are directed to a calibration unitcoupled with an equalizer and a detector, wherein the calibration unitis configured to jointly calibrate the equalizer and the detector usinga metric subject to an entropy-preserving equalizer constraint. Thecalibration unit is preferably configured to produce a decompositionthat satisfies the entropy-preserving equalizer constraint, such as byproducing a decomposition using a causal factor, an anticausal factor,and a delay factor. The calibration unit can be configured to producethe decomposition using a monic and minimum-phase factor, a monic andmaximum-phase factor, and a delay factor, a representative example ofwhich is given below.

In the following example, an equalizer f, such as an MRE equalizer f,has the following entropy-preserving normalization constraint in thefrequency domain:

${\log \; f_{\circ}} = {{\frac{1}{2\pi}{\int_{- \pi}^{\pi}{\log \; {{F(\omega)}}{\omega}}}} = 0}$

It is understood, however, any FIR f satisfying the above constraint canbe uniquely decomposed as:

f[n]=f _(c) [n]★f _(a) [n]★δ[n−d]

-   -   f_(c)[n]=causal, minimum-phase and monic f_(c)[0]=1    -   f_(a)[n]=anticausal, maximum-phase and monic f_(c)[0]=1    -   δ[n−d]=delay of d samples        The optimization is solved over the triplet (f_(c), f_(a), d)        which has simpler constraints.

Delay Optimization:

The optimal delay d needs to be determined before performing theadaptation. One approach to determining the optimal delay d involvesmanually searching over a range of values in the vicinity of the origin:−d_(max)≦d≦d_(max), d_(max)=1 or 2, although other approaches arecontemplated. In simulation environments, d is usually 0. This, however,is not guaranteed with real data since it depends on the timing recoveryblocks.

Numerical MRE Design Methodology:

Below is a representative example of a numerical MRE design algorithm inaccordance with various embodiments:

-   -   Collect long training sequences x₁ ^(N) and y₁ ^(N).    -   Pick an initial equalizer f[n]=δ[n].    -   repeat    -   Find the best μ(T) and p_(l)(T) for current f.    -   Find the best f and μ(T) for current p_(l)(T).    -   until convergence

We optimize over the DDNP means μ(T) in both steps since itsignificantly improves convergence rate.

Summary of MRE Design:

Summarizing the final result, the MRE design according to variousembodiments essentially solves:

$f_{MRE} = {\arg \; {\min\limits_{f}{\frac{1}{N_{T}}{\sum\limits_{T}{\frac{1}{2}\log \; {\sigma^{2}(T)}}}}}}$

where F(z)=z^(−d)F_(a)(z)F_(c)(z). It is noted that that σ²(T) is not asimple function of f. The term σ²(T) depends implicitly on f through theoptimal DDNP model parameters.

This problem is solved iteratively, such as in the following way:

-   -   1. For a given equalizer, the standard DDNP training is run.    -   2. For the resulting DDNP model, the equalizer is re-optimized.    -   3. This process is repeated until convergence.

FIG. 4 shows an embodiment of an apparatus 400 for performing jointcalibration using minimum relative entropy (MRE) in accordance withvarious embodiments. The embodiment shown in FIG. 4 includes anequalizer 420 and a detector 430 coupled to the equalizer 420. Theequalizer 420 receives a data signal y_(n) 415 from a channel 310. Thedata signal y_(n) 415 comprises a data-dependent noise component and auser information component x_(n) 305 with inter-symbol interference(ISI). The channel 310 can be a communication channel or a read channelof a magnetic recording device, for example. The detector 430 receivesan equalized signal z_(n) 425 from the equalizer 420 and performs anestimation of the user information component x_(n) 305 to achieve anestimate {circumflex over (x)}_(n) 435 of the user informationcomponent.

The detector 430 comprises a soft output Viterbi algorithm (SOVA) module432 and a data-dependent noise predictive (DDNP) module 434 coupled withthe SOVA module 432. The SOVA module 432 is configured to implement aViterbi algorithm and a trellis construct comprising states andtransitions among the states. The DDNP module 434 comprises a whiteningfilter and a storage device configured to store mean shifts for eachtransition in the trellis construct.

The apparatus 400 further includes a calibration unit 440 coupled withthe equalizer 420 and the detector 430. The calibration unit 440 isconfigured to jointly calibrate the equalizer 420 and the detector 430using the MRE metric. The MRE metric is used to find a modeled PDFmatching an actual PDF of the channel 310 as close as possible, tojointly calibrate the equalizer 420 and the detector 430. Thecalibration unit 440 is configured to determine the closest modeled PDFto the actual PDF of the channel from a class of modeled PDFs. Thedetermined PDF preferably has the minimum Kullback-Leibler distance tothe PDF of the channel. The calibration unit 440 comprises an algorithmmodule configured to provide updates to the equalizer 420 and thedetector 430. According to various embodiments, the joint calibrationunit 440 optimizes the equalizer 420 and the detector 430 with no needfor a two-step calibration and no need of a partial response (PR)target. The calibration unit 440 implements the metric of MRE or KLdistance, which is an optimal design metric.

Adaptive MRE Methodology:

FIG. 5 shows an embodiment of an apparatus for performing jointcalibration using minimum relative entropy (MRE) in accordance withvarious embodiments. In addition to the components shown in theembodiment of FIG. 4, the apparatus 500 illustrated in FIG. 5 includes astructure for implementing an adaptive MRE design. The equalizer 520comprises a causal equalizer F_(c) (z) 524 and an anti-causal equalizerz^(−d)F_(a)(z) 522. The calibration unit 540 implements an adaptivealgorithm module configured to provide updates to the equalizer 520 andthe detector 530 substantially in real-time.

A numerical MRE design algorithm discussed previously is suitable foroffline calibration since it requires all the training data to beavailable and it typically not suitable for real-time implementation.FIG. 5 illustrates an adaptive MRE design algorithm that uses asuboptimal MRE metric that is well-suited for simplified real-timeimplementations.

At a time n, the apparatus 500 computes all the following quantities:

-   -   applying filter 522 to y_(n)(515) yields y_(n) ^(a) (523):

$y_{n}^{a} = {\sum\limits_{l = 0}^{L_{a}}{f_{a,{- l}}y_{n + l - d}}}$

-   -   applying filter 524 to y_(n) ^(a) (523) yields equalized signal        z_(n) (525):

$z_{n} = {\sum\limits_{l = 0}^{L_{c}}{f_{c,l}y_{n - l}^{a}}}$

-   -   applying filter 526 to y_(n) ^(a) (523) for each T∈T yields        u_(n) ^(c)(T) (527):

${{u_{n}^{c}(T)} = {\sum\limits_{l = 0}^{L}{{w_{l}(T)}y_{n - l}^{a}}}},{\forall T}$

-   -   applying filter 516 to y_(n) (515) yields y_(n) ^(c) (517):

$y_{n}^{c} = {\sum\limits_{l = 0}^{L_{c}}{f_{c,l}y_{n + L_{a} - l - d}}}$

-   -   applying filter 518 to y_(n) ^(c) (517) for each T∈T yields        u_(n) ^(a)(T) (519):

${{u_{n}^{a}(T)} = {\sum\limits_{l = 0}^{L}{{w_{l}(T)}y_{n - l}^{c}}}},{\forall T}$

-   -   applying filter 528 to z_(n) (525) yields u_(n) (529):

$u_{n} = {\sum\limits_{l = 0}^{L}{{w_{l}\left( T_{n} \right)}z_{n - l}}}$

-   -   applying u_(n) (529) and μ(T_(n)) (551) to summer 552 yields        d_(n) (553):

d _(n) =u _(n)−μ(T _(n))

Having computed the above quantities, the calibration unit 540 performsall filter and mean updates. The updates include updates to:

-   -   the DDNP mean μ(T_(n))←μ(T_(n))+2a_(μ)d_(n)    -   the DDNP whitening taps        w_(l)(T_(n))←w_(l)(T_(n))−2a_(w)d_(n)z_(n l)    -   the causal equalizer factor f_(c,l)←f_(c,l)−2a_(c)d_(n)u_(n−l)        ^(a)(T_(u))    -   the anti-causal equalizer factor        f_(a,−1)←f_(a,−l)−2a_(a)d_(n)u_(n+l−L) _(o) ^(c)(T_(n))        The delayed quantities above, z_(n−l), u_(n−l) ^(a)(T_(n)), and        u_(n+l−L) _(a) ^(c)(T_(a)), are preferably stored and fetched        using buffers. It is noted that the step sizes a_(μ), a_(w),        a_(c) and a_(n) can be chosen independently. The best choice of        step sizes is typically found by simulations based on the actual        training data. The calibration unit 540 preferably comprises a        module implementing a least mean square (LMS) algorithm.

Variant Adaptive MRE Methodology:

FIG. 6 shows an embodiment of an apparatus for performing jointcalibration using minimum relative entropy in accordance with otherembodiments. The apparatus 600 illustrated in FIG. 6 includes astructure for implementing a variant adaptive MRE design of an equalizer620 and a detector 630 in accordance with various embodiments. Theapparatus 600 in FIG. 6 has a higher computational efficiency andsimpler implementation than the apparatus 500 in FIG. 5.

For example, and with reference once again to FIG. 5, the two filters518 and 526 {W_(T)(z)} represent a collection of filters (one for eachtransition in the trellis). Use of this collection of filters makes thecomputation of u_(n) ^(c)(T) (527) and u_(n) ^(a)(T) (519) for eachtransition T computationally expensive. The variant adaptive MREmethodology of FIG. 6 eliminates these signals and typically has a lowerimplementation complexity than the standard adaptive MRE architecturediscussed above. In particular, the variant adaptive MRE design shown inFIG. 6 has one collection of signals, {s_(n)(T)} as opposed to two{u_(n) ^(c)(T)} and {u_(n) ^(a)(T)} , and all updates are computed usingthe signals z_(n) and d_(n), and the signal collection {s_(n)(T)}.

In additional to the equalizer output z_(n) (625), and skipping theequivalent computations of FIG. 5 for simplicity of explanation, thefollowing computations are made by the variant adaptive MRE designimplemented by apparatus 600 at a time n:

-   -   the collection of signals, s_(n)(T) (627), is given by:

${{s_{n}(T)} = {\sum\limits_{l = 0}^{L}{z_{n - l}{w_{l}(T)}}}},{\forall T}$

-   -   the delay, d_(n) (653) is given by:

d _(n) =s _(n)(T _(n))−μ(T _(n))

-   -   the causal equalizer factor, Δc_(c,k), associated with filter        624 of the equalizer 620 is given by:

Δc_(c,k)=−2a _(c) d _(n) s _(n−k)(T _(n)), 1≦k≦L_(c)

-   -   the anti-causal equalizer factor, Δe_(a−k), associated with        filter 622 of the equalizer 620 is given by:

Δe_(a,−k)=−2a _(a) d _(n) s _(n+k)(T _(n)), 1≦k≦L_(a),

noting that the anti-causal factor expressions above depends on the samesignal, s_(n)(T) (627), that is already computed for the casual factorexpression.

Having computed the above quantities, the calibration unit 640 performsall filter and mean updates. The updates include updates to:

-   -   the filter F_(c)(z) 624 by        f_(c,l)←f_(c,l)−a_(c)(e_(c)*f_(c))_(l), 0≦l≦L_(c)    -   the filter F_(a)(z) 622 by        f_(a)(l)←f_(a,−1)−a_(a)(e_(a)*f_(a))⁻¹, 0≧l≧−L_(a)    -   the DDNP whitener W_(l)(T_(n))←W_(l)(T_(n))−a_(w)d_(n)z_(n−l),        0≦l≦L    -   the DDNP means μ(T_(n))←μ(T_(n))+a_(μ)d_(n)        The delayed quantities above, s_(n−k)(T_(n)) and s_(n+k)(T_(n)),        are preferably stored and fetched using buffers. It is noted        that the step sizes a_(μ), a_(w), a_(c) and a_(a) can be chosen        independently. The best choice of step sizes is typically found        by simulations based on the actual training data. The        calibration unit 640 preferably comprises a module implementing        a least mean square (LMS) algorithm.

The embodiments discussed herein above are described as using anentropy-based metric to jointly calibrate a channel equalizer anddetector. It is understood that a variety of statistical distancemeasures may be used in the context of various embodiments, includingany of the following: f-divergence, Hellinger distance, total variationdistance, Rényi's divergence, JensenShannon divergence, Lévy-Prokhorovmetric, Bhattacharyya distance, Wasserstein metric, energy distance,signal-to-noise ratio distance, Mahalanobis distance, distancecorrelation, continuous ranked probability scoring, andLukaszyk-Karmowski metric.

It is to be understood that even though numerous characteristics andadvantages of various embodiments disclosed herein have been set forthin the foregoing description, together with details of the structure andfunction of various embodiments, this detailed description isillustrative only, and changes may be made in detail, especially inmatters of structure and arrangements of parts within the principles ofthe presently disclosed subject matter to the full extent indicated bythe broad general meaning of the terms in which the appended claims areexpressed.

What is claimed is:
 1. An apparatus, comprising: an equalizer configuredto receive a data signal from a channel; a detector coupled to theequalizer; and a calibration unit coupled with the equalizer and thedetector, the calibration unit configured to jointly calibrate theequalizer and the detector using a metric subject to anentropy-preserving equalizer constraint.
 2. The apparatus of claim 1,wherein the calibration unit is configured to produce a decompositionthat satisfies the entropy-preserving equalizer constraint.
 3. Theapparatus of claim 2, wherein the calibration unit is configured toproduce the decomposition using a causal factor, an anticausal factor,and a delay factor.
 4. The apparatus of claim 2, wherein the calibrationunit is configured to produce the decomposition using a monic andminimum-phase factor, a monic and maximum-phase factor, and a delayfactor.
 5. The apparatus of claim 1, wherein the metric comprises anentropy-based metric.
 6. The apparatus of claim 1, wherein the metric isrepresentative of a statistical distance measure between a modeledprobability distribution functions (PDF) and an actual channel PDF. 7.The apparatus of claim 6, wherein the calibration unit is configured todetermine a PDF from a class of modeled PDFs using the statisticaldistance measure.
 8. The apparatus of claim 7, wherein the statisticaldistance measure comprises a Kullback-Leibler distance or relativeentropy.
 9. The apparatus of claim 1, wherein the detector comprises asoft output Viterbi algorithm (SOVA) module configured to implement aViterbi algorithm and a trellis construct comprising states andtransitions among the states.
 10. The apparatus of claim 9, wherein thedetector comprises a data-dependent noise predictive (DDNP) modulecoupled with the SOVA module.
 11. The apparatus of claim 10, wherein theDDNP module comprises a whitening filter and a storage device configuredto store mean shifts for each transition in the trellis construct. 12.The apparatus of claim 1, wherein the equalizer is configured to receivethe data signal from a read channel of a data storage device.
 13. Theapparatus of claim 1, wherein the equalizer is configured to performequalization without using a partial response target.
 14. A method,comprising: receiving a data signal from a channel by an equalizer;equalizing the data signal using the equalizer; detecting a userinformation component of the data signal using a detector; andcalibrating the equalizer and the detector jointly using anentropy-based metric subject to an entropy-preserving equalizerconstraint.
 15. The method of claim 14, wherein calibrating comprisesproducing a decomposition that satisfies the entropy-preservingequalizer constraint.
 16. The method of claim 15, wherein thedecomposition is produced using a causal factor, an anticausal factor,and a delay factor.
 17. The method of claim 14, wherein theentropy-based metric is representative of a statistical distance measurebetween a modeled PDF and an actual channel PDF, the statisticaldistance measure comprising a Kullback-Leibler distance or relativeentropy.
 18. The method of claim 14, wherein calibrating the equalizerand the detector jointly comprises providing updates to the equalizerand the detector adaptively and substantially in real-time.
 19. Themethod of claim 14, wherein the data signal is acquired from a magneticrecording medium.
 20. An apparatus, comprising: an equalizer configuredto receive a data signal having inter-symbol interference from achannel; and a detector coupled to the equalizer, the detector andequalizer configured to operate cooperatively to decode a userinformation component from the data signal without using a partialresponse target.